ere, we will blur in an image with a Gaussian Filter (effectively a low-pass filter) applied in the spatial frequency domain.

• First an image is imported
• The fourier transform of the image is then computed, and the image periodogram plotted.
• The fourier transform is multiplied by a Gaussian filter (this attenuates higher spatial frequencies - i.e. the finer detail is removed, leaving only the broad outline).
• The resulted is inverted to the image domain, giving a blurry image

This application uses the new Maple 2019 FFTShift function to swap data in a matrix or a vector into a different position. The Fourier transform of an image places lower frequency data near all four corners, with higher frequency data near the center. In this instance, FFTShift is typically applied to move the lowest frequencies to the center and the highest frequencies to the corners.

This results in a more meaningful visualization of the power spectrum where the lowest frequency data is contiguous, and simplifies the manipulation of image frequency data.